A laboratory ultracentrifuge is designed to produce a centripetal acceleration of 4.0 106 g at a distance of 5.00 cm from the axis. What angular velocity in rev/min is required?
Require R*w^2 = 4*10^6 g
Then solve for w, which will be in radians per second.
Then convert w to rpm.
Use an ^ before your exponents
R = 0.05 m
g = 9.8 m/s^2
Thank you drwls...
I got 2.7e6 but apparently that is incorrect.
To determine the angular velocity required for a centripetal acceleration, you can use the formula:
Centripetal acceleration (a) = Angular velocity (ω)² × Radius (r)
In this case, the centripetal acceleration is given as 4.0 × 10^6 g, which needs to be converted to meters per second squared (m/s²). One g is equal to approximately 9.8 m/s², so the centripetal acceleration can be expressed as:
a = (4.0 × 10^6) × (9.8 m/s²)
The radius is given as 5.00 cm, which needs to be converted to meters:
r = 5.00 cm = 0.05 m
Now, we can substitute the values into the formula:
(4.0 × 10^6) × (9.8 m/s²) = ω² × (0.05 m)
Simplifying the equation, we have:
(4.0 × 10^6 × 9.8) = 0.05 × ω²
Solving for ω²:
ω² = (4.0 × 10^6 × 9.8) / 0.05
Now, we can calculate ω:
ω = √[(4.0 × 10^6 × 9.8) / 0.05]
Finally, we need to convert the angular velocity to revolutions per minute (rev/min). To do this, we multiply ω by 60 (to convert seconds to minutes) and divide by 2π (since there are 2π radians in one revolution). Therefore:
ω (in rev/min) = ω (in rad/s) × (60 / 2π)
Substituting the value of ω, we can calculate the final answer.
Note: Please double-check the calculations to ensure accuracy.